Method To Design Polarization Arrangements For Mimo Antennas Using State Of Polarization As Parameter

ABSTRACT

The invention described herein provides a method of polarization based optimum constellation arrangements for modulation, multiplexing, diversity and spatio-temporal coding in wireless communication. The invention makes use of the polarization signal space to design optimal constellation arrangements, and to provide optimal State of Polarizations (SOPs) for Multiple-Input-Multiple-Output (MIMO) antennae for efficient diversity operations and for frequency re-use systems for multiplexing gains.

FIELD OF THE INVENTION

Present invention relates to wireless communication and morespecifically to wireless modulation, multiplexing and diversity schemes.

BACKGROUND OF THE INVENTION

1. Description of the Prior Art

It is an accepted fact that polarization of an electromagnetic signal isan underutilized parameter in wireless communication for modulation andmultiplexing, compared to, the other parameters such as amplitude,frequency and phase. Even though polarization has been usedconventionally as a diversity parameter, its usage has been limited tothe two orthogonal polarizations; mainly the linear horizontalpolarization (LHP) & linear vertical polarization (LVP) pair or righthanded circular polarization (RHCP) & left handed circular polarization(LHCP) pair. Same orthogonal polarization pairs have been used formultiplexing for the dual polarization frequency reuse systems fordoubling the capacity of the wireless link. An efficient crosspolarization interference canceller (XPIC) is one of the requirementsfor such operations. Even though polarization has been proposed and usedas a modulating parameter in optical communication, it is seldom used ina wireless communication link. This significantly unused polarizationspectrum is the resource that is being maximally and optimally utilizedin this present invention.

DISCLOSURE OF THE INVENTION

2. Summary of the Invention

The invention presented here relates to the use of State of Polarization(SOP) of an electromagnetic signal which can be used efficiently formodulation, multiplexing and diversity schemes as stand alone parametersor in conjunction with the other amplitude, phase, and frequencyparameters of an electromagnetic wave. The SOPs mentioned in thisinvention are different from the normally used LVP, LHP, RHCP, and LHCP.By using the unused polarizations of the polarization domain, theinvention makes use of the polarization signal space to design optimalconstellation arrangements, and to provide optimal SOPs forMultiple-Input-Multiple-Output (MIMO) antennae for efficient diversityoperations and for frequency re-use systems for multiplexing gains morethan 2.

It is an object of the present invention to provide a set ofpolarization constellation diagrams, for modulation, diversity ormultiplexing operations. Various arrangements different from prior artare given for 3 point, 4 point, 6 point and 8 point constellations.These constellations are marked on the Poincarésphere and each of theseconstellations have optimum and/or sub optimum properties as regards tothe cross polarization isolation (XPI), Euclidean distance and bit errorrate (BER).

When used in modulation such as M-array Polarization Shift Keying(MPolSK), these constellations act as the signal set for symbol mapping.When used in diversity/multiplexing operations of MIMO systems, theseconstellation points represent the SOP of the transmitting/receivingantennae.

It is a further object of the present invention to provide the systemsand circuits to generate these individual State of Polarizations (SOPs)and the constellation arrangements for wireless communication. Threedifferent ways of generating these polarizations or their constellationshave been provided in this invention. In the first approach,combinations of two orthogonal polarizations (linear or circular)antennae are used together with a signal processor at the base-band togenerate these polarizations. This approach is meant for MPolSK systemswhich introduce required SOPs for a sinusoidal signal. The secondapproach is also for a sinusoidal signal, where the signal processor atthe base-band is replaced by phase shifters and attenuators at the RF.These components introduce the required phase shift and amplitude to theorthogonal polarizations to generate the required SOP. In the thirdapproach, a means is described for polarizing a carrier modulated signalat RF. This approach is useful in MIMO systems.

It is further object of the invention to provide an advantageouslysimple Quaternary Polarization shift keying system (QPolSK) which usespolarization as the modulating parameter. In this object of theinvention, the demodulator and an optimum receiver design in the Stokesspace are provided.

It is a further object of the present invention to provide a co-channelmulti- polarization frequency reuse system employing more than 2polarizations for enhanced spectrum efficiency and for providing higherdata rate for a communication link. In the prior art, frequency re-usesystems employing 2 orthogonal polarization is the presented where asthis embodiment of the invention presents techniques for using more than2 polarizations for multiplexing (re-use) operation. This object of theinvention uses an optimally designed set of 3 or 4 polarizationstogether with suitable cross polarization interference cancellers andoffer 3 or 4 channels for multiplexing.

It is a further object of the invention to provide a mechanism to designorthogonal or substantially orthogonal polarizations for MIMO systems toenhance their performance. The antenna with the suggested polarizationswill be resulting in channels with uncorrelated fading which is arequirement for efficient reception at the receiver for MIMO systems. Bythis object of the invention, the spatial separation requirement in theorder of the many wavelengths required otherwise in the prior art can beeliminated. This allows the antennas to be closely located, moreantennae to be deployed and also facilitates antenna array with multiplebeams with each beam of separate polarization to be used in MIMOsystems. By this arrangement another degradation caused by varying angleof arrival also can be eliminated.

Still other objects and advantages of the present invention will becomereadily apparent to those skilled in this art from the detaileddescription, wherein only a preferred embodiment of the invention areshown and described, simply by way of illustration of the best modecontemplated to carry out the invention. As will be realized, theinvention is capable of other and different embodiments, and its severaldetails are capable of modifications in various obvious respects, allwithout departing from the invention.

BRIEF DESCRIPTION OF THE DRAWINGS signal.

FIG. 1. Poincarésphere representation of State of Polarization (SOP) ofan electromagnetic

FIG. 2. Poincarérepresentation angle pairs (2γ,δ) or (2ε,2τ)

FIG. 3. Stokes space parameters for representation of SOP

FIG. 4. Using orthogonal polarizations to generate any SOP; selection ofthe amplitudes and phases at base-band.

FIG. 5 Variable amplitude and phase using a phase shifter and attenuatorat RF.

FIG. 6. Carrier modulated signals and SOP selection

FIG. 7. Smart antenna for generating any pre-selected SOP

FIG. 8 Smart antennas at the receiver

FIG. 9. Antenna geometry of a square patch with one side as LHP and theother side as LVP.

FIG. 10. Variation, of S11 with frequency

FIG. 11. Radiation Pattern

FIG. 12. Physical parameters of the antennar

FIG. 13. 3 point constellation with 3 linear polarizations

FIG. 14. 3 point constellation with 2 linear polarizations and 1Circular polarization

FIG. 15. 3 Linearly polarized dipoles to generate the constellationdiagram of FIG. 13

FIG. 16. 4 point constellation with 2 RHEP polarizations and 2LHEPpolarizations.

FIG. 17. The BER performance for the constellation diagram given in 17.

FIG. 18. 4 point constellation with 3 elliptical polarizations and 1CP

FIG. 19. 4 point constellation with 2linear polarizations and 2CP

FIG. 20. 4 point constellation with 4 linear polarizations

FIG. 21. A simple quadrature polarization shift keying system forwireless

FIG. 22. 6 point constellation with 4 linear polarizations and 2CP

FIG. 23. 8 point constellation with 4 RHEP and 4LHEP

FIG. 24. BER performance of the 8 point constellation compared to thatof 8PSK

FIG. 25. Frequency re-use with 3 polarizations

FIG. 26. Frequency re-use with 4 polarizations

FIG. 27. Transmitter Antenna arrangement for a 3 in 3 out MIMO system(SOPs as in FIG. 14)

FIG. 28. Transmitter Antenna arrangement for a 3 in 3 out MIMO system(SOPs as in FIG. 13)

DESCRIPTION OF PREFERRED EMBODIMENT

To those skilled in the art, the invention admits of many variations.The following is a description of a preferred embodiment offered asillustrative of the invention but not restrictive of the scope of theinvention.

Polarization of an Electromagnetic signal describes the movement of theelectric field vector at one point in space as the wave progressesthrough that point. The tip of the electric field vector can trace aline resulting in linear polarization, a circle resulting in circularpolarization or more generally an ellipse, resulting in ellipticalpolarization. Polarization ellipse is the general representation and thelinear and circular polarizations are special cases of ellipticalpolarizations.

FIGS. 1, 2 and 3 describe the general state of art relating to thepolarization of an electromagnetic signal, representations of a signalor antenna including Poincarésphere and the Stokes space.

FIG. 1 shows a Poincarésphere [1] which can be used to represent theSOPs on graphical representation. The linear polarizations are on theequator [2], the left handed polarizations [3] on the upper hemisphere,and right handed polarizations [4] on the lower hemisphere. The NorthPole represents the LHCP [5] and South Pole represents the RHCP [6].

The points on the sphere are located using two pairs of angle which arerelated to each other, as shown in FIG. 2. The pair of angle used are

-   -   1. (γ,δ) pair where 2γ is the great circle distance from the LHP        [7] point and δ is the angle of the great circle with respect to        the equator [2].    -   2. (2τ,2ε) pair where 2τ is the longitude [9]and 2ε is the        latitude [10].

Any SOP can be represented mathematically as the combination of twoorthogonal linear polarizations {right arrow over (E)}_(x) and {rightarrow over (E)}_(x).{right arrow over (E)} _(x) =a ₁cos(τ+δ₁)  (A){right arrow over (E)} _(y) =a ₂cos(τ+δ₂)  (B)where a₁ and a₂ are their respective amplitudes andδ=δ₂−δ₁  (c)is the phase difference between the y component of the electric fieldwith respect to the x component. The angle γ is given by $\begin{matrix}{\gamma = {\tan^{- 1}\left( \frac{a_{2}}{a_{1}} \right)}} & (D)\end{matrix}$

FIG. 3 shows another useful representation of SOP known in literature asStokes parameters representation. Following the description in (B), fora signal with the {Ex, Ey, Ez} defined by $\begin{matrix}\left. \begin{matrix}{{E_{x} = {a_{1}{\cos\left( {\tau + \delta_{1}} \right)}}},} \\{{E_{y} = {a_{2}{\cos\left( {\tau + \delta_{2}} \right)}}},} \\{E_{z} = 0}\end{matrix} \right\} & (E)\end{matrix}$the Stokes parameters are given by $\begin{matrix}\left. \begin{matrix}{{s_{0} = {a_{1}^{2} + a_{2}^{2}}},} \\{{s_{1} = {a_{1}^{2} - a_{2}^{2}}},} \\{{s_{2} = {2\quad a_{1}a_{2}\cos\quad\delta}},} \\{s_{3} = {2\quad a_{1\quad}a_{2}\sin\quad\delta}}\end{matrix} \right\} & (F)\end{matrix}$

Any elliptically polarized SOP can be generated by using 2 linearlypolarized components (LHP [7] & LVP [8]) of appropriate amplitudes andrelative phases. Another method for representing and generating theseSOPs are by using two RHCP [6] and LHCP [5] components of appropriateamplitudes and phase shift. If the media involves ionosphere, linearcomponents may be affected by Faraday rotation, whereas circularlypolarized components are immune to the rotation. A method to decomposeany SOP into (LVP [8] and LHP [7]) or (RHCP [6] and LHCP [5]) isillustrated in (C). All the methods of implementation involve an arrayof two elements which generate the LHP [7], LVP [8] signals ofappropriate amplitude and phases or alternatively LHCP [5], RHCP [6]signals. If the orthogonal polarizations are selected as the LHP [7],LVP [8] combination, the antenna structure will henceforth be called asOrthogonal Linear Combination Array (OLCA) [11]. If the orthogonalpolarizations are the LHCP [5], RHCP [6] combination, the antennastructure will henceforth be called as Orthogonal Circular CombinationArray (OCCA) [12]. An OLCA [11] or an OCCA [12] is a 2 element antennaarray which can generate any SOP based on the amplitude and phase of thesignal at its input ports. Such an antenna is described in detail infurther below.

Various forms of realization of the required SOPs are shown in the FIGS.4, 5, 6, and 7. In FIG. 4, the required SOP is generated by an OLCA [11]or an OCCA [12] with the selection of the suitable amplitude and phasefrom a look up table which is performed at the base-band [13]. Thisimplementation is meant for a sinusoidal signal which is usually thecase with a Polarization shift keying systems. The processor [14] in thebase band will be reading the amplitude and phase values for both thechannels and the sinusoidal signals of these amplitudes and phases willbe generated by using a direct wireless synthesizer or any othersuitable means, and later, up converted to the higher RF range by the upconverter mixer.

In FIG. 5, another implementation for a sinusoidal signal is shown. Herethe amplitude and phase shifts are performed in RF and are suitable forPolarization shift keying systems which do not employ a processor [14]at the base-band [13]. The phase shifting and amplitude selection can becontrolled electronically by using suitable continuous time or discretetime circuits.

In FIG. 6, the signal to be polarized is a carrier modulated signal. Inthis case, if ‘m’ [15] State of Polarizations are needed, the radiatingmechanism should be a polarization agile antenna generating ‘m’ [15]beams with each having different polarization sense or a collection of‘m’ [15] smart antenna elements each with different SOPs. An intelligent‘n’ [16] to ‘m’ [15] mapping circuit will map the carrier modulatednarrow band signals to their respective SOPs based on some predefinedcriteria. Such an arrangement is suitable for the frequency reusesystems, MIMO systems and polarization diversity schemes.

A polarization agile smart antenna which can polarize a narrow bandsignal to any pre-selected SOP is shown in FIG. 7. It consists of apower divider [8], which splits the power equally into 2 in-phasebranches. The amplitudes and phases of these branches are then modified(using predetermined scaling and shifting values) which are determinedby the required SOP. These scaled and shifted signals are then fed tothe two ports of a OLCA [11] or an OCCA [12] which in the far field willgenerate the required SOP.

These modifications are later corrected at the receiver side toregenerate the original carrier modulated signal.

Such a smart antenna [17] at the receiver side is shown in FIG. 8. Here,the amplitudes and phases of the received signals are corrected by usingthe same proportion to cancel the changes introduced at the transmitter.The received RF signal is usually then fed to the mixer/down converterfor the receiver signal processing. The single element planar antennawhich performs as an OLCA [11] is described in this embodiment of theinvention. This antenna is called as Dual port Micro strip line fedsquare patch antenna.

FIG. 9 shows the structure of the dual port square patch antenna for thefrequency range 2.4 GHz. The resonating frequency and operatingbandwidth are: TABLE 1 Resonating frequency and operating band of theLHP [7] feed and LVP [8] feed Port Resonating Frequency GHz OperatingBand % Bandwidth Port 1 2.455 2.515-2.395 4.9 Port 2 2.4075  2.36-2.4553.9

FIG. 10 shows the variation of S11 for both the ports. It can be seenthat the antenna offers a good bandwidth at these frequencies.

FIG. 11 shows the radiation pattern of the antenna with the ports ofexcitation being port 1 [19] and port 2 [20] separately.

The physical parameters of the antenna are shown in FIG. 12.

-   Dimension L×W=30×30 mm²-   Substrate dielectric constant εr=4.28-   Thickness h=1.6 mm.

The antenna is found to resonate at 2.455 GHz at port 1 and at 2.4075GHz at port 2 [20].

In this part of the invention, novel constellation arrangements inpolarization signal space intended for wireless communicationapplications are presented. These constellation arrangements and theconstituent SOPs are different from the polarizations used in wirelesscommunication in the prior art. In the prior art, the polarization usedfor signal or antennae are mainly the LHP [7], LVP [8], +45 linear, RHCP[6], and LHCP [5]. Occasionally elliptical polarization is used but, theposition of the SOP of such elliptical polarization on a Poincaréspherewas inconsequential for such applications. In this part of theinvention, every constellation diagram is followed by the constituentLHP [7], LVP [8] amplitude and phases required for its generation usingan OLCA [11].

The constellation arrangements employing three points in thepolarization signal space which provide advantageous benefits to awireless communication system are shown in FIG. 13 and FIG. 14.

The constellation arrangement in FIG. 13 shows three points in thepolarization signal space with maximum Euclidean distance of 1. 73 on aunit sphere. These SOPs provide maximum isolation among themselves andwhen used in Polarization shift keying schemes, they provide maximum BERperformance due to the maximum Euclidean distance.Poincarérepresentation angle pairs (2γ,δ) or (2ε,2τ) for the 3 points ofconstellation in FIG. 13 are given below: TABLE 2 Points (all angles indegrees) 2ε 2τ 2γ δ S₁ S₂ S₃ α₁ α₂ δ P₁ 0 0 0 0 1 0 0 1 0 0 P₂ 0 120 1200 −0.5 0.866 0 −0.5 0.866 0 P₃ 0 240 240 0 −0.5 −0.866 0 −0.5 −0.866 0

The Stoke's parameters of these SOPs are given in the same table. Theamplitudes of the LHP [7] component, a₁ and LVP [8] component a₂ and therelative phase difference between them δ=δ₂−δ₁ are also provided in thetable. The value of δ is the angle by which the γ component leads the xcomponent. The 3 points P1, P2, P3 can be represented mathematically as;

-   -   P1:        {right arrow over (E)} _(x)(t)=1.({right arrow over (x)} cos        ωt))        {right arrow over (E)} _(y)(t)=0  (G1)    -   P2:        {right arrow over (E)} _(x)(t)=−0.5({right arrow over (x)}        cos(ωt))        {right arrow over (E)} _(y)(t)=0.866({right arrow over (x)}        cos(ωt))  (G2)    -   P3:        {right arrow over (E)} _(x)(t)=−0.5({right arrow over (x)}        cos(ωt))        {right arrow over (E)} _(y)(t)=−0.866({right arrow over (x)}        cos(ωt+90°))  (G3)

The 3 polarizations are linear polarizations and the antennae for such acombination can be designed easily. 3 dipoles, one in horizontaldirection, one in +60° to the horizontal and another one 120° to thehorizontal can generate these polarizations. Essential data for the 3point constellation in FIG. 14 is given below: TABLE 3 Points 2ε 2τ 2γ δS₁ S₂ S₃ α₁ α₂ δ P₁ 0 0 0 0 1 0 0 1 0 0 P₂ 90 90 90 90 0 0 1 0.707 0.70790 P₃ 0 180 180 0 −1 0 0 0 1 0

Such an arrangement is shown in FIG. 15. One another method to generatethese SOPs is to use a LHP [7] antenna for P1, a LOCA for P2 and anotherLOCA for P3.

Another 3 point constellation on Poincarésphere is provided in FIG. 14.It uses two orthogonal linear polarizations and a left handed circularpolarization (could as well be RHCP [6]). An advantage of thisarrangement is the ease of generating these polarizations. The twolinear polarizations are the commonly used LHP [7] and LVP [8] for whichmany antennae are available of the shelf for most of the frequencies. Togenerate the CP, another set of LHP [7] and LVHP [5] are required with afixed attenuator and phase shifter as shown in FIG. 7 or anyconventional circular polarized antenna can be used thus eliminating theneed for new design and fabrication. However, the Euclidean distance isonly 1.414 in this case compared to the 1.73 of the previousarrangement.

-   -   P1:        {right arrow over (E)} _(x)(t)=1({right arrow over (x)} cos(ωt))        {right arrow over (E)} _(y)(t)=0  (H1)    -   P2:        {right arrow over (E)} _(x)(t)=0.707({right arrow over (x)}        cos(ωt))        {right arrow over (E)} _(y)(t)=0707({right arrow over (x)}        cos(ωt+90°))  (H2)    -   P3:        {right arrow over (E)} _(x)(t)=0        {right arrow over (E)} _(y)(t)=1({right arrow over (x)}        cos(ωt))  (H3)

Two 4 point optimal constellation arrangements are shown in FIG. 16 andFIG. 17 both these arrangements provide a maximum Euclidean distance of1.663 on a unit sphere. An analysis of the constellation set in FIG. 6is performed here for determining its performance for an AWGN channelwhen used for M-PolSK modulation. Such modulations can be used where thedepolarizing effect of the channel is minimum such as inter-satellitelinks.

Consider the symmetrically arranged 4 points on the Poincarésphere shownin FIG. 16. Points on the upper plane are called High Plane 1 (HP1) andHigh Plane 2 (HP2). Points on the lower hemisphere are called Low Plane1 (LP1) and Low plane 2 (LP2) respectively. Their Poincarérepresentationparameters, stokes parameters and the orthogonal component amplitudesand phases are given below: TABLE 4 Points 2ε 2τ 2γ δ S₁ S₂ S₃ α₁ α₂ δP₁ 35.26 0 35.26 90 0.8166 0 0.5773 0.9530 0.3028 90 P₂ −35.26 90 90−35.26 0 0.8166 −0.5773 0.7071 0.7071 −35.26 P₃ 35.26 180 144.7 90−0.8166 0 0.5773 0.3028 0.9530 90 P₄ −35.26 270 90 −144.7 0 −0.81660.5773 0.7071 0.7071 −144.7

It should be noted that these four points are at maximum Euclideandistance (d_(min)) between each other given byd _(min)=2√{square root over (2)}/√{square root over (3)}

These 4 points are elliptically polarized with HP1 and HP2 as lefthanded elliptically polarized, and LP1 and LP2 as right handedelliptically polarized. The electrical vectors of these 4 points arecompletely described by their amplitudes and relative phase differenceswhich can be easily found from the Stokes parameters. The constituentelectric vectors are given by the following equations for these fourpoints at the z=0 plane.

-   -   P1:        {right arrow over (E)} _(x)(t)=0.953({right arrow over (x)} cos        ωt)        {right arrow over (E)} _(y)(t)=0.303{{right arrow over (x)}        cos(ωt+90°)}  (I1)    -   P2:        {right arrow over (E)} _(x)(t)=0.707({right arrow over (x)} cos        ωt)        {right arrow over (E)} _(y)(t)=0.707{{right arrow over (x)}        cos(ωt−35.27°)}  (I2)    -   P3:        {right arrow over (E)} _(x)(t)=0.303({right arrow over (x)} cos        ωt)        {right arrow over (E)} _(y)(t)=0.953{{right arrow over (x)}        cos(ωt+90°)}  (I3)        and    -   P4:        {right arrow over (E)} _(x)(t)=0.707({right arrow over (x)} cos        ωt)        {right arrow over (E)} _(y)(t)=0.707{{right arrow over (x)}        cos(ωt−144.7°)}  (I4)

The elliptically polarized SOPs can be generated by using 2 linearlypolarized components of appropriate amplitudes and relative phases.Another method for representing and generating these SOPs are by usingtwo RHCP [6] and LHCP [7] components of appropriate amplitudes and phaseshift. A method to decompose any SOP into RHCP [6] and LHCP [5] isstraight forward [C] and following the standard method; the four pointscan be split as shown below.

-   -   HP1:        {right arrow over (E)} _(L)(t)=0.6283({right arrow over (x)} cos        ωt−{right arrow over (y)} sin ωt)        {right arrow over (E)} _(R)(t)=0.3248({right arrow over (x)} cos        ωt+{right arrow over (y)} sin ωt)  (J1)    -   HP2:        {right arrow over (E)} _(L)(t)=0.6283({right arrow over (x)} cos        ωt−{right arrow over (y)} sin ωt)        {right arrow over (E)} _(R)(t)=0.3248{{right arrow over (x)}        cos(ωt+π)+{right arrow over (y)} sin(ωt+π)}        =−0.3248{{right arrow over (x)} cos(ωt)+{right arrow over (y)}        sin(ωt)}  (J2)    -   LP1: $\begin{matrix}        {{{{\overset{->}{E}}_{L}(t)} = {0.3248\left( {{\overset{->}{x}\cos\quad\omega\quad t} - {\overset{->}{y}\sin\quad\omega\quad t}} \right)}}\begin{matrix}        {{{\overset{->}{E}}_{R}(t)} = {0.6283\left\{ {{\overset{->}{x}\cos\quad\left( {{\omega\quad t} + \frac{\pi^{\circ}}{2}} \right)} + {\overset{->}{y}\sin\quad\left( {\omega\quad + \frac{\pi^{\circ}}{2}} \right)}} \right\}}} \\        {= {0.6283\left\{ {{{- \overset{->}{x}}{\sin\left( {\omega\quad t^{\circ}} \right)}} + {\overset{->}{y}{\cos\left( {\omega\quad t^{\circ}} \right)}}} \right\}}}        \end{matrix}} & ({J3})        \end{matrix}$        and LP2: $\begin{matrix}        {{{{\overset{->}{E}}_{L}(t)} = {0.3248\left( {{\overset{->}{x}\cos\quad\omega\quad t} - {\overset{->}{y}\sin\quad\omega\quad t}} \right)}}\begin{matrix}        {{{\overset{->}{E}}_{R}(t)} = {0.6283\left\{ {{\overset{->}{x}\cos\quad\left( {{\omega\quad t} + {3\frac{\pi}{2}}} \right)} + {\overset{->}{y}\sin\quad\left( {{\omega\quad t} + {3\quad\frac{\pi^{\circ}}{2}}} \right)}} \right\}}} \\        {= {{- 0.6283}\left\{ {{\overset{->}{x}{\cos\left( {\omega\quad t} \right)}} + {\overset{->}{y}{\sin\left( {\omega\quad t} \right)}}} \right\}}}        \end{matrix}} & ({J4})        \end{matrix}$

It should be noted that for the points HP1 and HP2, the LHCP [5] vectoris stronger than the RHCP [6], indicating left handed ellipticalpolarization. Similarly, for the points LP1 and LP2, the RHCP [6]components are stronger indicating a right handed ellipticalpolarization. Another important point to note here is that, all thesepoints can be generated by a signal set of 3 vectors given byu ₁(t)=({right arrow over (x)} cos ωt−{right arrow over (y)} sin ωt)u ₂(t)=({right arrow over (x)} cos ωt+{right arrow over (y)} sin ωt)u ₃(t)=(−{right arrow over (x)} sin ωt°+{right arrow over (y)} cosωt)°  (K)

The vector u₃(t) is basically u₂(t) with a 90° phase shift. In the nextsection, these three vectors will be used as an orthogonal basis set torepresent the four constellation points.

Orthogonal circular polarizations are used to generate the four points.It can be implemented by using two radiators which are RHGP [6] and LHCP[5] with proper amplitudes and phase difference. These amplitudes andphase difference are given below: TABLE 5 Amplitude and phase for a OCCA[12] to generate the constellation in FIG. 16 Point E_(R) E_(L) Phase(θ_(R)-θ_(L))° HP1 0.6283 0.3248 0 HP2 0.6283 0.3248 180 LP1 0.32480.6283 90 LP2 0.3248 0.6283 270

The receiver is based on a receiving antenna where the SOP of theantenna is determined by the relative amplitude and phase of theconstituent circular polarizations. The implementation of this circuitcan be performed based on a signal processor as the controller togetherwith the radiating elements. The received SOPs are fed to a Stokes spacereceiver for optimum detection.

The signal space for the proposed constellation, arrangement can berepresented by three orthogonal basis functions which can be identifiedfrom the constituent vectors used to represent the constellation points.They are given by equation (K). Orthogonality of these functions can beverified easily. Normalizing these basis functions yield their amplitudeasA=¹ /√{square root over (T)} _(s)where T_(S) is the symbol time. The three ortho-normal signals can beused to represent each of the constellation points ass(t)=a ₁ u ₁(t)+a ₂ u ₂(t)+a ₃ u ₃(t)  (L)

This space can be superimposed onto the Stokes space and properselection of T_(S) can result in the set {a₁,a₂,a₃} to be same as theStokes parameters given in Table 4. For the points on the unit sphere,with √{square root over (E)}_(s)=1 and${d_{\min} = \frac{2\quad\sqrt{2}}{\sqrt{3}}},$the set of coordinates of each point is given as below. $\begin{matrix}{{{{HP}\quad 1\text{:}\quad\left\{ {{d_{\min}/2},0,{{d_{\min}/2}\sqrt{2}}} \right\}}{HP}\quad 2\text{:}\quad\left\{ {{{- d_{\min}}/2},0,{{d_{\min}/2}\sqrt{2}}} \right\}}{{LP}\quad 1\text{:}\quad\left\{ {0,{d_{\min}/2},{{{- d_{\min}}/2}\sqrt{2}}} \right\}\quad{and}}{{LP}\quad 2\text{:}\quad\left\{ {0,{{- d_{\min}}/2},{{{- d_{\min}}/2}\sqrt{2}}} \right\}}} & (M)\end{matrix}$

Let n₁, n₂, n₃ be the relevant noise components along the three axeswith zero mean and variance σ²=η/2. It will be convenient to calculatethe probability of correct decision p_(c) and then determine theprobability of symbol error as p_(s)=1−p_(c).

Assuming that the point HP2 is transmitted, the probability of a correctdecision is given by $\begin{matrix}\begin{matrix}{{P\left( {C/{HP}_{2}} \right)} = {\left( {\frac{1}{\sqrt{\left( {\pi\quad\eta} \right)}}{\int_{- \infty}^{d/2}{{\mathbb{e}}^{{- n_{1}^{2}}/\eta}{\mathbb{d}n_{1}}}}} \right)\left( {\frac{1}{\sqrt{\left( {\pi\quad\eta} \right)}}{\int_{{- d}/2}^{d/2}{{\mathbb{e}}^{{- n_{2}^{2}}/\eta}{\mathbb{d}n_{2}}}}} \right)}} \\{\left( {\frac{1}{\sqrt{\left( {\pi\quad\eta} \right)}}{\int_{{- \frac{d}{2}}\sqrt{2}}^{\infty}{{\mathbb{e}}^{{- n_{3}^{2}}/\eta}{\mathbb{d}n_{3}}}}} \right)} \\{= {\left( {1 - {Q\left( \frac{d}{\sqrt{\left( {2\quad\eta} \right)}} \right)}} \right)\left( {1 - {2\quad{Q\left( \frac{d}{\sqrt{\left( {2\quad\eta} \right)}} \right)}}} \right)\left( {1 - {Q\left( \frac{d}{2\sqrt{\eta}} \right)}} \right)}}\end{matrix} & (N)\end{matrix}$

Assuming an equi-probable transmission of symbols, the symbol errorprobability of the system is given byp _(e)(s)=1−p(c/HP ₂)  (O)

The equation (H) can be expressed in terms of the bit energy E_(b) asshown below.

The Euclidean distance is related to the symbol energy (radius of thesphere) as $\begin{matrix}{{d = {\frac{2\quad\sqrt{2}}{\sqrt{3}}\sqrt{E_{s}}}}{d^{2} = {\frac{16}{3}E_{b}}}} & (P)\end{matrix}$

Substituting this into equation (H), and replacing η=N_(o)$\begin{matrix}\begin{matrix}{{p_{e}(s)} = {1 - \left\lbrack \left( {1 - {Q\left( {\frac{2\sqrt{2}}{\sqrt{3}}\sqrt{\frac{E_{b}}{N_{o}}}} \right)}} \right) \right.}} \\\left. {\left( {1 - {2{Q\left( {\frac{2\sqrt{2}}{\sqrt{3}}\sqrt{\frac{E_{b}}{N_{o}}}} \right)}}} \right)\left( {1 - {Q\left( {\frac{2}{\sqrt{3}}\sqrt{\frac{E_{b}}{N_{o}}}} \right)}} \right)} \right\rbrack\end{matrix} & (Q)\end{matrix}$

The above equation gives the BER performance in a closed form. This isplotted against that of QPSK in FIG. 17.

The four polarization constellation set shown in FIG. 18 also showssimilar properties. Having the same Euclidean distance as the 16, thissignal space also provides a similar BER performance. TABLE 6 Essentialdata for the 4 point constellation in FIG. 18 Points 2ε 2τ 2γ δ S₁ S₂ S₃α₁ α₂ δ P₁ 90 90 90 90 0 0 1 0.707 0.707 90 P₂ −19.475 0 19.45 −900.9428 0 −0.3333 0.9855 0.1691 −90 P₃ −19.475 120 118.12 −22.21 −0.47130.8165 −0.3333 0.5141 0.8577 −22.21 P₄ −19.475 240 118.12 −157.8 −0.4713−0.8165 −0.3333 0.5141 0.8577 −157.8

FIG. 19 and the below table 7 give another useful set of SOPs which are2 linear and 2 circular. TABLE 7 Essential data for the 4 pointconstellation in FIG. 19 Points 2ε 2τ 2γ δ S₁ S₂ S₃ α₁ α₂ δ P₁ 0 0 0 0 10 0 1 0 0 P₂ 0 180 180 0 −1 0 0 0 1 0 P₃ −90 90 90 90 0 0 −1 0.707 0.70790 P₄ 90 90 90 −90 0 0 1 0.707 0.707 −90

They are useful when used in 4 in 4 out MIMO systems with simple off theshelf antenna for transmission and reception. FIG. 20 and thecorresponding below Table 8 represent another such advantageously simplearrangement employing 4 linear polarizations. TABLE 8 Essential data forthe 4 point constellation in FIG. 20 Points 2ε 2τ 2γ δ S₁ S₂ S₃ α₁ α₂ δP₁ 0 0 0 0 1 0 0 1 0 0 P₂ 0 180 180 0 −1 0 0 0 1 0 P₃ 0 90 90 0 0 1 00.707 0.707 0 P4 0 270 270 180 0 −1 0 0.707 0.707 180

An advantageously simple quadrature polarization shift keying modulationfor wireless communication is provided here. Block diagram of thissystem is given in FIG. 21.

The phase shifter [21] in the upper channel [22] provides the followingphase shift. I bit at 1 phaseshift = δ₁ Output at 2 0  0° cos(ω_(c)t) 190° cos(ω_(c)t + 90°)

The phase shifter [21] in the lower channel [23] provides the followingphase shift. Q bit at 3 phaseshift = δ₂ Output at 4 0 −90° cos(ω_(c)t −90°) 1  90° cos(ω_(c)t + 90°)

These outputs are fed to a LHP-LVP combination antenna. The SOPsgenerated can be seen in the FIG. 19. This structure is one of thesimplest QPolSK which can be used for many applications.

A novel constellation arrangement for 6 points is shown in FIG. 22. Itscorresponding information is given below in Table 9. The Euclideandistance is 1.414 in this arrangement on a unit sphere. TABLE 9Essential data for the 6 point constellation in FIG. 22 Points 2ε 2τ 2γδ S₁ S₂ S₃ α₁ α₂ δ P₁ 0 0 0 0 1 0 0 1 0 0 P₂ 0 180 180 0 −1 0 0 0 1 0 P₃0 90 90 0 0 1 0 0.707 0.707 0 P4 0 270 270 180 0 −1 0 0.707 0.707 180 P5−90 90 90 90 0 0 −1 0.707 0.707 90 P6 90 90 90 −90 0 0 1 0.707 0.707 −90

A constellation diagram with 8 spherically symmetric points on thePoincarésphere is shown in FIG. 23. Points on the upper hemisphere arecalled HP1, HP2, HP3 and HP4. Points on the lower hemisphere are calledLP1, LP2, LP3, and LP4. These points are arranged on a unit sphere(√{square root over (E)}_(x)=1) with the maximum Euclidean distance of$d_{\min} = {\frac{2}{\sqrt{3}}.}$

Other relevant information on this constellation is given in below inTable 10. TABLE 10 Essential data for the 8 point constellation in FIG.23 Points 2ε 2τ 2γ δ S₁ S₂ S₃ α₁ α₂ δ P₁ 35.26 0 35.26 90 0.8166 00.5773 0.9530 0.3028 90 P₂ 35.26 90 90 35.26 0 0.8166 0.5773 0.70710.7071 35.26 P₃ 35.26 180 144.7 90 −0.8166 0 0.5773 0.3028 0.9530 90 P435.26 270 90 144.7 0 −0.8166 0.5773 0.7071 0.7071 144.7 P5 −35.26 4554.73 −45 0.5773 0.5773 −0.5773 0.8881 0.4597 −45 P6 −35.26 135 125.27−45 −0.5773 0.5773 −0.5773 0.4597 0.8881 −45 P7 −35.26 225 125.27 −135−0.5773 −0.5773 −0.5773 0.4597 0.8881 −135 P8 −35.26 315 54.73 −1350.5773 −0.5773 −0.5773 0.8881 0.4597 −135

The signal space for the above constellation arrangement can berepresented by the same three orthogonal basis functions discussed insection V, given by equation (K). For the points on the unit sphere,with √{square root over (E)}_(s)=1 and${d_{\min} = \frac{2}{\sqrt{3}}},$the set of coordinates of each point is given as below. $\begin{matrix}{{{HP}\quad 1\text{:}\quad\left\{ {{d_{\min}/\sqrt{2}},0,{d_{\min}/2}} \right\}}{{HP}\quad 2\text{:}\quad\left\{ {0,{d_{\min}/\sqrt{2}},{d_{\min}/2}} \right\}}{{HP}\quad 3\text{:}\quad\left\{ {{{- d_{\min}}/\sqrt{2}},0,{d_{\min}/2}} \right\}}{{HP}\quad 4\text{:}\quad\left\{ {0,{{- d_{\min}}/\sqrt{2}},{d_{\min}/2}} \right\}}{{LP}\quad 1\text{:}\quad\left\{ {{d_{\min}/2},{d_{\min}/2},{{- d_{\min}}/2}} \right\}}{{LP}\quad 2\text{:}\quad\left\{ {{{- d_{\min}}/2},{d_{\min}/2},{{- d_{\min}}/2}} \right\}}{{LP}\quad 3\text{:}\quad\left\{ {{{- d_{\min}}/2},{{- d_{\min}}/2},{{- d_{\min}}/2}} \right\}}{{LP}\quad 4\text{:}\quad\left\{ {{d_{\min}/2},{{- d_{\min}}/2},{{- d_{\min}}/2}} \right\}}} & (R)\end{matrix}$

Let n₁, n_(2,) n₃ be the relevant noise components along the three axeswith zero mean and variance σ²=η−/2. It will be convenient to calculatethe probability of correct decision P_(c) and then determine theprobability of symbol error as p_(s)=1−p_(c).

Assuming that the point HP3 is transmitted, the probability of a correctdecision is given by $\begin{matrix}\begin{matrix}{{P\left( {C/{HP}_{3}} \right)} = {\left( {\frac{1}{\sqrt{\left( {\pi\quad\eta} \right)}}{\int_{- \infty}^{d/2}{{\mathbb{e}}^{{- n_{1}^{2}}/\eta}{\mathbb{d}n_{1}}}}} \right)\left( {\frac{1}{\sqrt{\left( {\pi\quad\eta} \right)}}{\int_{{- d}/2}^{d/2}{{\mathbb{e}}^{{- n_{2}^{2}}/\eta}{\mathbb{d}n_{2}}}}} \right)}} \\{\left( {\frac{1}{\sqrt{\left( {\pi\quad\eta} \right)}}{\int_{{- d}/2}^{\infty}{{\mathbb{e}}^{{- n_{3}^{2}}/\eta}{\mathbb{d}n_{3}}}}} \right)} \\{= {\left( {1 - {Q\left( \frac{d}{\sqrt{\left( {2\quad\eta} \right)}} \right)}} \right)\left( {1 - {2\quad{Q\left( \frac{d}{\sqrt{\left( {2\quad\eta} \right)}} \right)}}} \right)\left( {1 - {Q\left( \frac{d}{\sqrt{\left( {2\quad\eta} \right)}} \right)}} \right)}}\end{matrix} & (S)\end{matrix}$

Assuming an equi-probable transmission of symbols, the symbol errorprobability of the system is given byp _(e)(s)=1−p(c/HP ₃)

The equation can be expressed in terms of the bit energy E_(b) as shownbelow.

The Euclidean distance is related to the symbol energy (radius of thesphere) as $d = {\frac{2}{\sqrt{3}}\sqrt{E_{s}}}$$d^{2} = {{\frac{4}{3}\left( {3\quad E_{b}} \right)} = {4\quad E_{b}}}$

Substituting this into (S), and replacing η=N_(o) $\begin{matrix}{{p_{e}(s)} = {1 - \left\lbrack {\left( {1 - {Q\left( {\sqrt{2}\sqrt{\frac{E_{b}}{N_{o}}}} \right)}} \right)\left( {1 - {2{Q\left( {\sqrt{2}\sqrt{\frac{E_{b}}{N_{o}}}} \right)}}} \right)\left( {1 - {Q\left( {\sqrt{2}\sqrt{\frac{E_{b}}{N_{o}}}} \right)}} \right)} \right\rbrack}} & (T)\end{matrix}$

The above equation gives the symbol error performance in a closed formand it is compared to that of 8PSK[24] in the FIG. 24. It can be seenthat, there is a considerable improvement in symbol error performance ofthe proposed system. The improvement in performance for an error rate of10⁻⁴ is around 1 dB compared to an 8 PSK[24] system.

Using polarization as a multiplexing parameter results in co channelcross polarized frequency reuse systems. Prior art has shown that byusing two orthogonal polarizations such as LHP [7], LVP [8] pair,+45degree pair or LHCP [5], RHCP [6] pair, two channels for datatransmission can be obtained for the same frequency band, thus offeringtwo times the data rate. This embodiment of the present inventionextends the frequency reuse to 3 and 4 parallel channels. The optimumpolarizations have been provided for both the cases and theirperformance evaluated.

A tri-polarized co channel frequency reuse system employs 3 separateantennae to transmit and receive 3 different data streams to achieve adata rate which is 3 times that of a SISO system. Block diagram of sucha system is shown in FIG. 25. These systems employ 3 different antennaeof 3 different SOPs which offer maximum cross polarization isolation.The optimum SOPs of the antennas are shown in the constellation FIGS. 13and 14. The receiver employs an adaptive equalizer which computes thechannel state information apriori to the transmission of data and usespilot symbol insertion to train the adaptive filter. Once the adaptationhappens, the receiver is expected to fully know the channel. The sameantenna structure can be used at the receiver to receive the signal.

Assume a channel which offers flat fading for the frequency band ofinterest. The channel input output for this system can be modeled asr=√{square root over (E)} _(x) H _(i,j) x+n  (U)which can be written in matrix form as $\begin{matrix}{\begin{bmatrix}r \\r_{1} \\r_{2}\end{bmatrix} = {{{\sqrt{E_{s}}\begin{bmatrix}{h_{0,0}h_{0,1}h_{0,2}} \\{h_{1,0}h_{1,1}h_{1,2}} \\{h_{2,0}h_{2,1}h_{2,2}}\end{bmatrix}}{X\begin{bmatrix}x_{0} \\x_{1} \\x_{2}\end{bmatrix}}} + n}} & (V)\end{matrix}$where n is the WSS noise with IID components.

The matrix H_(i,j) is conventionally called the channel matrix of a MIMOsystem. When used in frequency re-use using multiplexing in thepolarization domain, the matrix can be called as polarization matrix.

Here we assume that the transmitter and receiver use the samepolarization. The actual values of the coefficients depend on thepropagation conditions. These values are expected to be complex gaussianrandom variables with a mean value shown in the matrix above. Forsimplicity of analysis, we can assume that $\begin{matrix}{{ɛ\left\{ {h_{0,0}}^{2} \right\}} = {{ɛ\left\{ {h_{1,1}}^{2} \right\}} = {{ɛ\left\{ {h_{2,2}}^{2} \right\}} = {1\quad{and}}}}} & (W)\end{matrix}$

The ensemble average of the cross coupled components as their mean valuem_(i,j). Cross polarization discrimination of the channel and theantennae determine these coefficients. By using an antenna of high XPD,it is possible to achieve a small value for the average componentm_(i,j). The total XPD of each cross coupled branch can be representedbyh _(i,j(total)) =h _(i,j(static)) +m _(i,j,i≠j)  (X1)  (x1)andH _(i,j) =H _(i,j(static)) +└m _(i,j)┘  (X2)

The H_(i,j(static)), which describes the inherent cross coupling betweenthe polarizations employed can be computed from the Polarizationsemployed for the frequency re-use. These matrices are dependent on thechosen SOPs and their position on the sphere. By using standard methodsof computing the cross polar isolation, these values can be easilyfound.

At the receiver, the channel estimation can be used with any of theknown methods of the prior art cross polarization interferencecancellation methods to remove the cross polarized component toregenerate the three different data streams. The channel estimation isperformed by a suitable adaptive filter algorithm such as the LMS or RLSalgorithm. Analysis and design procedures of the adaptive filter andcross polarization interference canceller are abundant in prior art. Themajor difference here is in the H matrix where, in the dual polarizedsystems described in prior art, the H matrix is described byH _(i,j) =H _(i,j(static)) +└m _(i,j)┘  (Y1)

With H_(i,j(static)) being an identity matrix giving rise to$\begin{matrix}{H_{i,j} = \begin{bmatrix}{1,m_{0,1},m_{0,2}} \\{{m_{1,0}1},m_{1,2}} \\{m_{2,0}m_{2,1}1}\end{bmatrix}} & ({Y2})\end{matrix}$

When it is assumed that m_(i,j)=m_(j,1)=α and all cross polarized termsto be equal, we get a matrix channel as $\begin{matrix}{H_{i,j} = \begin{bmatrix}{1,\alpha,\alpha} \\{\alpha,1,\alpha} \\{\alpha,\alpha,1}\end{bmatrix}} & ({Y3})\end{matrix}$

In the system presented here, the cross polarization components arebigger due to the non-identity H_(i,j(static)) matrix. However, as theindividual values of these cross polar elements (the non-diagonalelements of H_(i,j(static))) are known apriori, the contribution ofthese components can be subtracted at the receiver to generate a systemwhich is equal in performance to the dual polarized frequency re-usesystems of the prior art.

A quad-polarized co channel frequency reuse system employs 4 separateantennae to transmit and receive 4 different data streams to achieve adata rate which is 4 times that of a SISO system.

Block diagram of such a system is shown in FIG. 26. These systems employ4 different antennae of 4 different SOPs which offer maximum crosspolarization isolation. They are shown in the constellation FIGS. 16 and17 and other 4 point constellations of this invention. The receiveremploys an adaptive equalizer which computes the channel stateinformation apriori to the transmission of data and uses pilot symbolinsertion to train the adaptive filter. Once the adaptation happens, thereceiver is expected to fully know the channel.

Assume a channel which offers flat fading for the frequency band ofinterest. The channel input output for this system can be modeled asr=√{square root over (E)} _(s) H _(i,j) x+n

Which can be written in matrix form as $\begin{matrix}{\begin{bmatrix}r \\r_{1} \\r_{2} \\r_{4}\end{bmatrix} = {{{\sqrt{E_{s}}\begin{bmatrix}h_{0,0} & h_{0,1} & h_{0,2} & h_{0,3} \\h_{1,0} & h_{1,1} & h_{1,2} & h_{1,3} \\h_{2,0} & h_{2,1} & h_{2,2} & h_{2,3} \\h_{3,0} & h_{3,1} & h_{3,2} & h_{3,3}\end{bmatrix}} \times \begin{bmatrix}x_{0} \\x_{1} \\x_{2} \\x_{3}\end{bmatrix}} + n}} & \left( {Z\quad 1} \right)\end{matrix}$Where n is the WSS noise with IID components.

The matrix H_(i,j) is conventionally called the channel matrix of a MIMOsystem. When used in frequency re-use using multiplexing in thepolarization domain, the matrix can be called as polarization matrix.

Here we assume that the transmitter and receiver use the samepolarization. The actual values of the coefficients depend on thepropagation conditions and the polarizations chosen. These values areexpected to be complex gaussian random variables with a mean given bym_(i,j). For simplicity of analysis, we can assume thatɛ{h_(0, 0)²} = ɛ{h_(1, 1)²} = ɛ{h_(2, 2)²} = 1  andthe ensemble average of the cross coupled components as their mean valuem_(i,j). Cross polarization discrimination of the channel and theantennae determine these coefficients. By using an antenna of high XPD,it is possible to achieve a small value for the average componentm_(i,j). The total XPD of each cross coupled branch can be representedbyh _(i,j(total)) =h _(i,j(static)) +m _(i,j,i≠j)andH _(i,j) =H _(i,j(static)) +└m _(i,j)┘  (Z2)

The H_(i,j(static)) can be computed from the Polarizations employed forthe frequency re-use. At the receiver, the channel estimation can beused with any of the known methods of the prior art cross polarizationinterference cancellation methods to remove the cross polarizedcomponent to regenerate the three different data streams.

This object of the invention can result in more than 1 or 2 antenna atthe receiver and more than 3 or 4 antennae at the transmitter thusoffering a diversity gain up to 64. When used with proper STTC design,the system will offer unprecedented coding gain as well. In prior art,MIMO antenna installation and the number of antenna elements have beenseverely restricted by the inter element spacing of nearly 10 lambda,where lambda is the wavelength of the signal. The large spacing wasrequired because base stations were usually mounted on elevatedpositions where the presence of local scatterers to offer uncorrelatedscattering cannot be guaranteed always. This has limited the number ofantenna to be 2, 3 or 4. The shorter length or separation at the mobileterminal is due to the presence of local scatterers resulting inuncorrelated fading always. However, for handsets, fitting of even twoantennae is not advisable due to the aesthetical requirement of embeddedantennae.

In this embodiment of the present invention, the antennae of differentstates of polarization are suggested to be used. When used in MIMOsystems, these antennae with optimally selected SOPs offering a highdegree of cross polarization isolation provide channels withuncorrelated fading even when the inter element spacing is less than 1lambda for outdoor and 0.1 lambda for indoor. Hence, this presentembodiment facilitates a closer placement of the antennae when used fordiversity/multiplexing and/or state time trellis or block coding. Thisis an advantageous benefit as the space requirement for antennaeinstallation can be minimal, the problems associated with varying angleof arrival can be avoided and a suitable radome can be designed for theprolonged life of the antennae.

Fading experienced by different polarizations have known to beuncorrelated in both urban, semi urban or rural situations and hasmaintained this property for both indoor and outdoor wireless channels.

This embodiment of the present invention facilitates toe following

-   1. To reduce the inter element antenna spacing to less than 1 lambda    at the base station-   2. To employ upto 8 antenna of different SOPs at the transmitter.    The optimum SOPs for 2, 3, 4, 6, and 8 antenna at transmit or    receive or both terminals are given in the corresponding    constellation diagrams.-   3. To employ 2, 3, 4, 6 or 8 antennae of different SOP at the    receiver.-   4. To offer a transmit diversity of up to 64 (8 Tx. and 8 Rx.)-   5. To offer up to 8 multiplexing channels with or without the use of    adaptive modulation and space time coding.

As an example, the transmitting side antenna configuration of 3 in 3 outMIMO system employing the antennas of SOPs corresponding to FIG. 13 isshown in FIG. 25. A similar antenna configuration at the receiver cangive rise to 3 in 3 out MIMO system where the antennas can be closelyspaced compared to the present structures where there is a minimumdistance between the antennas. FIG. 26 shows the transmitting sideantenna configuration when the antennas used are having the SOPs shownin FIG. 13. Similar arrangements are given in FIGS. 27 and 28.

By employing such antennas of optimally selected SOPs, the MIMOconfiguration of higher order can be employed. This is an advantageoussituation compared to the previous art.

1. A method of wireless communication based on multiplexing in a systemof multiple-input-multiple-output antennas, comprising: selecting aplurality of states of polarization; providing antenna arrays capable ofgenerating signals of the selected states of polarization; transmittingsignals simultaneously by multiplexing in a plurality of channels,wherein each channel of the plurality of channels is assigned to one ofthe plurality of states of polarization.
 2. The method according toclaim 1, wherein the step of selecting a plurality of states ofpolarization comprises: maximizing the Euclidian distances between theplurality of states of polarization on the Pointcaré sphere.
 3. Themethod according to claim 1, wherein the step of providing antennaarrays capable of generating signals of the selected states ofpolarization comprises: providing a set of antennas of orthogonalpolarization.
 4. The method according to claim 3, wherein the set ofantennas of orthogonal polarization are connected to a signal processor.5. The method according to claim 3, wherein the set of antennas oforthogonal polarization is connected to a power divider, discretephase-shifter and attenator to change the polarization of signal fornarrow-band modulating.
 6. The method according to claim 1, wherein thestep of transmitting signals comprises generating of RF-signals withrequired states of polarization.
 7. The method according to claim 1,wherein the step of transmitting signals comprises polarizationmodulating.
 8. The method according to claim 1, wherein the number ofthe plurality of channels is three or more.
 9. The method according toclaim 2, wherein the plurality of states of polarization on saidPointcaré sphere comprises P1, P2 and P3 with the electric vectors{right arrow over (E)}_(x) and {right arrow over (E)}_(y) given by: P1:{right arrow over (E)} _(x)(t)=1{{right arrow over (x)} cos(107 t)}{right arrow over (E)} _(y)(t)=0 P2:{right arrow over (E)} _(x)(t)=−0.5{{right arrow over (x)} cos(ωt)}{right arrow over (E)} _(y)(t)=−0.866{{right arrow over (x)} cos(ωt)}and P3:{right arrow over (E)} _(x)(t)=−0.5{{right arrow over (x)} cos(ωt)}{right arrow over (E)} _(y)(t)=−0.866{{right arrow over (x)}cos(ωt+90°)}.
 10. The method according to claim 2, wherein the pluralityof states of polarization on said Pointcaré sphere comprises P1 to P4with the electric vectors {right arrow over (E)}_(x) and {right arrowover (E)}_(y) given by: P1:{right arrow over (E)} _(x)(t)=0.953({right arrow over (x)} cos ωt){right arrow over (E)} _(y)(t)=0.303{{right arrow over (x)} cos(ωt+90°)}P2:{right arrow over (E)} _(x)(t)=0.707({right arrow over (x)} cos(ωt){right arrow over (E)} _(y)(t)=0.707{{right arrow over (x)}cos(ωt−35.27°)} P3:{right arrow over (E)} _(x)(t)=0.303({right arrow over (x)} cos ωt){right arrow over (E)} _(y)(t)=0.953{{right arrow over (x)} cos(ωt+90°)}and P4:{right arrow over (E)} _(x)(t)=0.707({right arrow over (x)} cos ωt){right arrow over (E)} _(y)(t)=0.707{{right arrow over (x)}cos(ωt−144.7°)}.
 11. The method according to claim 2, wherein theplurality of states on said Pointcaré sphere comprises P1 to P4 with theelectric vectors {right arrow over (E)}_(x) and {right arrow over(E)}_(y) given by: P1:{right arrow over (E)} _(x)(t)=0.707({right arrow over (x)} cos ωt){right arrow over (E)} _(y)(t)=0.707{{right arrow over (x)} cos(ωt+90°)}P2:{right arrow over (E)} _(x)(t)=0.9855({right arrow over (x)} cos ωt){right arrow over (E)} _(y)(t)=0.1691{{right arrow over (x)}cos(ωt−90°)} P3:{right arrow over (E)} _(x)(t)=0.5141({right arrow over (x)} cos ωt){right arrow over (E)} _(y)(t)=0.8577{{right arrow over (x)}cos(ωt−22.21°)}and P4:{right arrow over (E)} _(x)(t)=0.5141({right arrow over (x)} cos ωt){right arrow over (E)} _(y)(t)=0.8577{{right arrow over (x)}cos(ωt−157.8°)}.
 12. The method according to claim 2, wherein theplurality of states on said Pointcaré sphere comprises P1 to P4 with theelectric vectors {right arrow over (E)}_(x) and {right arrow over(E)}_(y) given by: P1:{right arrow over (E)} _(x)(t)=1.0({right arrow over (x)} cos ωt){right arrow over (E)} _(y)(t)=0){{right arrow over (x)} cos(ωt+0°)} P2:{right arrow over (E)} _(x)(t)=0)({right arrow over (x)} cos ωt){right arrow over (E)} _(y)(t)=1.0{{right arrow over (x)} cos(ωt+0°)}P3:{right arrow over (E)} _(x)(t)=0.707({right arrow over (x)} cos ωt){right arrow over (E)} _(y)(t)=0.707{{right arrow over (x)} cos(ωt+90°)}and P4:{right arrow over (E)} _(x)(t)=0.707({right arrow over (x)} cos ωt){right arrow over (E)} _(y)(t)=0.707{{right arrow over (x)}cos(ωt−90°)}.
 13. The method according to claim 2, wherein the pluralityof states on said Pointcaré sphere comprises P1 to P4 with the electricvectors {right arrow over (E)}_(x) and {right arrow over (E)}_(y) givenby: P1:{right arrow over (E)} _(x)(t) =1.0({right arrow over (x)} cos ωt){right arrow over (E)} _(y)(t)=(0){{right arrow over (x)} cos(ωt+0°)}P2:{right arrow over (E)} _(x)(t) =0)({right arrow over (x)} cos ωt){right arrow over (E)} _(y)(t)=1.0{{right arrow over (x)} cos(ω t+0°)}P3:{right arrow over (E)} _(x)(t) =0.707({right arrow over (x)} cos ωt){right arrow over (E)} _(y)(t)=0.707{{right arrow over (x)} cos(ωt+0°)}and P4:{right arrow over (E)} _(x)(t) =0.707({right arrow over (x)} cos ωt){right arrow over (E)} _(y)(t)=0.707{{right arrow over (x)}cos(ωt+180°)}.
 14. The method according to claim 2, wherein theplurality of states comprises P1 to P6 with the electric vectors {rightarrow over (E)}_(x) and {right arrow over (E)}_(y) given by: P1:{right arrow over (E)} _(x)(t) =1.0({right arrow over (x)} cos ωt){right arrow over (E)} _(y)(t)=(0){{right arrow over (x)} cos(ωt+0°)}P2:{right arrow over (E)} _(x)(t) =0)({right arrow over (x)} cos ωt){right arrow over (E)} _(y)(t)=1.0{{right arrow over (x)} cos(ωt+0°)}P3:{right arrow over (E)} _(x)(t) =0.707({right arrow over (x)} cos ωt){right arrow over (E)} _(y)(t)=0.707{{right arrow over (x)} cos(ωt+0°)}P4:{right arrow over (E)} _(x)(t) =0.707({right arrow over (x)} cos ωt){right arrow over (E)} _(y)(t)=0.707{{right arrow over (x)}cos(ωt+180°)} P5:{right arrow over (E)} _(x)(t) =0.707({right arrow over (x)} cos ωt){right arrow over (E)} _(y)(t)=0.707{{right arrow over (x)} cos(ωt+90°)}and P6:{right arrow over (E)} _(x)(t) =0.707({right arrow over (x)} cos ωt){right arrow over (E)} _(y)(t)=0.707{{right arrow over (x)}cos(ωt−90°)}.
 15. The method according to claim 2, wherein the pluralityof states on said Pointcaré sphere comprises P1 to P8 with the electricvectors {right arrow over (E)}_(x) and {right arrow over (E)}_(y) givenby: P1:{right arrow over (E)} _(x)(t) =0.953({right arrow over (x)} cos ωt){right arrow over (E)} _(y)(t)=(0.302{{right arrow over (x)}cos(ωt+90°)} P2:{right arrow over (E)} _(x)(t) =0.707({right arrow over (x)} cos ωt){right arrow over (E)} _(y)(t)=0.707{{right arrow over (x)}cos(ωt+35.26°)} P3:{right arrow over (E)} _(x)(t) =0.3028({right arrow over (x)} cos ωt){right arrow over (E)} _(y)(t)=0.9530{{right arrow over (x)}cos(ωt+90°)} P4:{right arrow over (E)} _(x)(t) =0.707({right arrow over (x)} cos ωt){right arrow over (E)} _(y)(t)=0.707{{right arrow over (x)}cos(ωt+144.7°)} P5:{right arrow over (E)} _(x)(t) =0.888({right arrow over (x)} cos ωt){right arrow over (E)} _(y)(t)=0.4597{{right arrow over (x)}cos(ωt−45°)} P6:{right arrow over (E)} _(x)(t) =0.4597({right arrow over (x)} cos ωt){right arrow over (E)} _(y)(t)=0.8881{{right arrow over (x)}cos(ωt−45°)} P7:{right arrow over (E)} _(x)(t) =0.4597({right arrow over (x)} cos ωt){right arrow over (E)} _(y)(t)=0.8881{{right arrow over (x)}cos(ωt−135°)}and P8:{right arrow over (E)} _(x)(t) =0.8881({right arrow over (x)} cos ωt){right arrow over (E)} _(y)(t)=0.4597{{right arrow over (x)}cos(ωt−135°)}.
 16. Device for transmitting and/or receiving adapted forwireless communication according to the method of claim 1.